The present invention relates to a method of designing a cavity shape of a mold by utilizing solidification analysis particularly for obtaining an optimum cavity shape free from shrinkage cavities in the resulting cast products.
In the solidification analysis by numerical calculation, a system including a casting and a mold is generally represented by a two-dimensional or three-dimensional model consisting of small elements, and the temperature change of all small elements is calculated to conduct the solidification analysis of a casting to be produced.
In the case of the two-dimensional model, the number of steps of preparing the model, the number of calculation steps and calculation cost are small. However, since heat transfer in a three-dimensional direction is not taken into account, its calculation accuracy is inevitably low.
On the other hand, in the case of the three-dimensional model, the calculation accuracy is high due to a three-dimensional approximation, but the model is so large that the number of steps of preparing the model is extremely large, and that the calculation for solid fraction takes too much time, resulting in higher cost of calculation.
In addition, in both two-dimensional model and three-dimensional model, calculation is conducted not only on the casting but also on the mold, leading to enormous numbers of calculation steps. Also, to increase the calculation accuracy, portions in which temperature changes largely should be divided into smaller elements, and in the case of using a sand mold having a small thermal conductivity, smaller elements should be made on the mold near the casting. These matters also lead to larger numbers of calculation steps.
As a means for temperature distribution analysis with reduced number of calculation steps, a heat flux method is known (Eisuke Niiyama, "Castings," Vol. 49, No. 10, 1977). In the heat flux method, the calculation of a mold is eliminated, and the heat flux on a casting surface is numerically calculated with simple boundary conditions taken into account.
In the heat flux method, it is assumed that the casting surface has a constant temperature. However, in a practical casting process, the temperature on the casting surface changes with time in most cases, except for the casting of pure metals without excess heat. As a result, the calculation accuracy is inevitably low. In addition, since an air gap between the casting and the mold is not taken into account, the heat flux method cannot be applied to die casting in which this air gap shows great influence.